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What Are The Pump Affinity Laws?

Engineers specifying centrifugal pumps for their application are typically most concerned with the three primary performance characteristics: flow, head, and power. These three characteristics all vary in orderly fashion with changes in impeller speed, following very simple equations. These equations are known as the pump affinity laws and allow for the prediction of pump performance at varying speeds. Given flow, head, and power at one speed for a specific pump, one can determine new values for those parameters at a different speed.

The first pump affinity law deals with flow, or pump capacity. The flow varies in direct proportion with the impeller speed. If the impeller speed for a particular pump is increased by 10%, the flow from that pump increases by 10%. Likewise, if the impeller speed is reduced by 20%, the flow is reduced by 20%. The affinity law equation for flow is:

{\frac{Q_1}{Q_2} = \frac{N_1}{N_2}}

Where N1 = Original speed, Q1 = Original flow, N2 = New speed, Q2 = New flow. Rearranging we get

{Q_2 = Q_1 \times \frac{N_2}{N_1}}

The second pump affinity law deals with fluid head. The head that a particular pump generates varies with the square of the proportional speed change. For head, when the impeller speed is increased by 10%, the head is increased by 21% and so on. The affinity law equation for head is:

{\frac{H_1}{H_2} = \left(\frac{N_1}{N_2}\right)^2}

Where N1 = Original speed, H1 = Original head, N2 = New speed, H2 = New head. Rearranging we get

{H_2 = H_1 \times \left(\frac{N_2}{N_1}\right)^2}

The third pump affinity law deals with hydraulic power. The power that a particular pump generates varies with the cube of the proportional speed change, and thus is most impacted by speed adjustments. The affinity law equation for power is:

{\frac{P_1}{P_2} = \left(\frac{N_1}{N_2}\right)^3}

Where N1 = Original speed, P1 = Original power, N2 = New speed, P2 = New power. Rearranging we get

{P_2 = P_1 \times \left(\frac{N_2}{N_1}\right)^3}

Using the equations above, a single point or even an entire pump curve can be adjusted to find out how the pump in question will perform at a different speed. This is especially helpful when looking at the possible applicability and benefits of using a Variable Speed Drive.